It is commonplace in hydrocarbon production for the fluid produced by a well to be a mixture of two phases: oil and water. As a general rule the water constitutes the continuous phase while the oil constitutes the dispersed phase which is in the form of bubbles.
Conventional techniques for analyzing flows in hydrocarbon wells are based on measuring the total flow rate Q.sub.t and the water holdup H.sub.w (i.e. the mean static fraction of the water). It is conventional to use a spinner flowmeter that responds to velocity for measuring the total flow rate Q.sub.t, and use a differential pressure apparatus responsive to density and called a pressure gradiometer for measuring the water holdup H.sub.w. The oil flow rate Q.sub.o is determined from these measurements by the conventional formula: EQU Q.sub.o =(1-H.sub.w) (Q.sub.t +V.sub.S .multidot.H.sub.w.multidot. S)
where V.sub.S is the slip velocity between the phases and S is the cross-sectional area of the well.
The above formula assumes that the values of velocity and holdup that result from the above-mentioned measurements, which are mean values over the flow section, are indeed representative of the flow. In other words, the variations in velocity and water holdup across the section of the well are negligible, or in any event have a negligible overall influence on the result.
That assumption is justified for a well that is vertical. However, for an inclined well the difference in density between the phases tends to cause them to separate: water which is the heavier phase predominates in the lower part of the flow section whereas oil which is lighter predominates in the upper part of the section. Under certain conditions, the phases separate completely, i.e. the lower part of the flow section is occupied solely by water while the upper part is occupied solely by oil (reference may be made on this topic to the Society of Petroleum Engineers (SPE) article #18217 entitled "Oil/water Flow Structure Measurements in Inclined Pipes", 2-5 Oct. 1988, by P. Vigneaux, G. Catala, and J. P. Hulin). In this type of situation, backflow is observed in the bottom of the flow section.
Naturally, under such conditions, given that the variations in water holdup and in velocity across the flow section are large, the results obtained by the abovementioned measurements do not provide a reliable estimate of the looked-for mean values.